The Peierls-Nabarro barrier is a discrete effect that frequently occurs in discrete nonlinear systems. A signature of the barrier is the slowing and eventual stopping of discrete solitary waves. This work examines intense electromagnetic waves propagating through a periodic honeycomb lattice of helically driven waveguides, which serves as a paradigmatic Floquet topological insulator. Here it is shown that discrete topologically protected edge modes do not suffer from the typical slowdown associated with the Peierls-Nabarro barrier. Instead, as a result of their topological nature, the modes always move forward and redistribute their energy: a narrow (discrete) mode transforms into a wide effectively continuous mode. On the other hand, a discrete edge mode that is not topologically protected does eventually slow down and stop propagating. Topological modes that are initially narrow naturally tend to wide envelope states that are described by a generalized nonlinear Schrödinger equation. These results provide insight into the nature of nonlinear topological insulators and their application.

中文翻译：

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非线性Floquet拓扑绝缘子的Peierls-Nabarro势垒效应。

Peierls-Nabarro势垒是一种离散效应，在离散非线性系统中经常发生。障碍的标志是离散的孤立波的减速和最终停止。这项工作研究了通过螺旋驱动波导的周期性蜂窝网格传播的强电磁波，该周期性蜂窝网格充当了典型的Floquet拓扑绝缘体。在此表明，离散的拓扑保护边缘模式不会受到与Peierls-Nabarro势垒相关的典型减速的影响。相反，由于其拓扑性质，这些模式始终向前移动并重新分配其能量：窄（离散）模式转换为宽有效的连续模式。另一方面，离散边缘模式不是受拓扑保护的确最终会放慢速度并停止传播。最初很窄的拓扑模式自然会趋向于由广义非线性Schrödinger方程描述的宽包络状态。这些结果提供了对非线性拓扑绝缘子的性质及其应用的了解。